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CABARRUS COUNTY 2012 APPRAISAL MANUAL The question we really want to ask is are the two distributions the same (in the sense that the distribution of parcels by age makes them equal for purposes of judging similarities) or are the distributions different. To answer this, we must consider the element of chance. It is possible that the sales are distributed like the total area but show difference in cell frequencies due to chance alone, for as you may observe, the percentages of the total by age are indeed different. We would expect the sales to be distributed in like frequencies as the total area was distributed unless the sales do not represent the area under study. The use of a very handy tool, the statistic known as the CHI - SQUARE (X test, is worth learning. It is useful in that it does not require that one have normally distributed data to be valid; hence it is non parametric. It is used by taking an expected frequency and comparing it to the actual or observed frequency. In our case, it is the area parameters projected upon the sales data. We would expect the number of sale parcels per age group to be the same as the frequencies observed for the total of all parcels in the hypothetical area under consideration. Therefore, we use the percentages for the total to generate the expected number of sales for each age interval. The CHI - SQUARE statistic expressed as a formula is: 100.0% 76. The actual number of sales in each interval is set down. One then subtracts the estimated number from the observed number of sales, interval by interval, squaring the result and dividing by the expected number. Example: GROUP OBSERVED EXPECTED x2 =y [(fo- fe)2 /fe] SQUARED DIVIDED BY where fo = frequency observed FREQUENCY FREQUENCY fe = frequency expected RESULT EXPECTED Example: 1 10 09.3 0.70 EXPECTED NUMBER PERCENT OF TOTAL OF SALES IN TOTAL PARCEL x SALES = EACH INTERVAL 12.2 76 9.3 22.4 76 17.0 33.9 76 25.8 13.3 76 10.1 8.3 76 6.3 9_9 76 7_5 100.0% 76. The actual number of sales in each interval is set down. One then subtracts the estimated number from the observed number of sales, interval by interval, squaring the result and dividing by the expected number. Example: GROUP OBSERVED EXPECTED OBSERVED SQUARED DIVIDED BY FREQUENCY FREQUENCY MINUS EXPECTED RESULT EXPECTED 1 10 09.3 0.70 00.49 0.053 2 22 17.0 5.00 25.00 1.471 3 17 25.8 8.80 77.44 3.002 4 10 10.1 0.10 00.10 0.010 5 07 06.3 0.70 00.49 0.053 6 10 07.5 2.50 06.25 0.833 X = 5.422 Cabarrus County — 2012 Revaluation STATISTICS & THE APPRAISAL PROCESS 10-11 8/9/11 Attachment number 11 G -6 Page 306